Is the mean bacteria colonies count in the west basin of Lake Macatawa less than 10? Suppose 34 samples of water were taken from the west basin. The mean colonies count in these samples was 11.95 with the variance 153.76. What is the power of the test if the true mean count is 7.4?

a) 0.41

b) 0.62

c) 0.06

d) 0.84

e) none of the answers provided here

The University of Cincinnati Center for Business Analytics is an outreach center that collaborates with industry partners on applied research and continuing education in business analytics. One of the programs offered by the center is a quarterly Business Intelligence Symposium. Each symposium features three speakers on the real-world use of analytics. Each of the corporate members of the center (there are currently 10) receives twelve free seats to each symposium. Nonmembers wishing to attend must pay $75 per person. Each attendee receives breakfast, lunch, and free parking. The following are the costs incurred for putting on this event:

(1 point) Use the Normal Approximation to the Binomial Distribution to compute the probability of passing a true/false test of 40 questions if the minimum passing grade is 90% and all responses are random guesses.

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 75 and estimated standard deviation σ = 31. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)


What is the probability that x(mean) < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

An economics professor randomly selected 100 millionaires in the United States. The average age of these millionaires was 54.8 years. The population standard deviation is known to be 7.9 years. What is the 95% confidence interval for the mean age, of all United States millionaires? Interpret the confidence interval.

Point Estimate: ______

Critical Value:

Margin of Error: ________

Confidence Interval:______

Interpretation:

****show spss input***A researcher is interested to learn if the level of interaction a women in her 20s has with her mother influences her life satisfaction ratings. Below is a list of women who fit into each of four levels of interaction. Conduct a One-way ANOVA on the data to determine if there are differences between groups; does the level of interaction influence women’s ratings of life satisfaction? Report the results of the One-way ANOVA. If significance is found, run the appropriate post-hoc test and report between what levels the significant differences were found. Report the test statistic using correct APA formatting and interpret the results.

2. Are handedness and gender related? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05. Report the test statistic using correct APA formatting and interpret the results.

The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used for a specific purpose requires an average cut-on voltage of 0.60 V, and if this is not achieved, the amount of impurity must be adjusted. A sample of diodes was selected and the cut-on voltage was determined. The accompanying SAS output resulted from a request to test the appropriate hypotheses. [Note: SAS explicitly tests

H₀: μ = 0,

so to test

H₀: μ = 0.60,

the null value 0.60 must be subtracted from each

x_i;

the reported mean is then the average of the

(x_i − 0.60)

values. Also, SAS's P-value is always for a two-tailed test.]

What would be concluded for a significance level of 0.01?

Reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting.

Reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.    

Do not reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.

What would be concluded for a significance level of 0.05?

Reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting. Reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.    

Do not reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.

What would be concluded for a significance level of 0.10?

Reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting.

Reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.   

Do not reject the null hypothesis. There is sufficient evidence to conclude that the amount of impurities needs adjusting.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the amount of impurities needs adjusting.

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 250 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.4% and standard deviation σ = 1%.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.4%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =

Sampling Distributions:

Explain the difference between the uniform and normal probability distributions. Give a real-life example

The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

1. Use α = 0.01 to test the hypotheses

for the model

y = β₀ + β₁x₁ + β₂x₂ + ε,

where

1b. Find the value of the test statistic. (Round your answer to two decimal places.)

1c. Find the p-value. (Round your answer to three decimal places.)

p-value =

1d. State your conclusion.

(a) Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b) Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.    

(c) Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

(d) Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.

2. Use α = 0.05 to test the significance of β₁.

2a. State the null and alternative hypotheses.

2b. Find the value of the test statistic. (Round your answer to two decimal places.)

2c. Find the p-value. (Round your answer to three decimal places.)

p-value =

2d. State your conclusion.

(a) Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(b) Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.    

(c) Reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(d) Reject H₀. There is insufficient evidence to conclude that β₁ is significant.

2e. Should x₁ be dropped from the model?

Yes

No

3.Use α = 0.05 to test the significance of β₂.

3a. State the null and alternative hypotheses.

3b. Find the value of the test statistic. (Round your answer to two decimal places.)

3c. Find the p-value. (Round your answer to three decimal places.)

p-value =

3d. State your conclusion.

(a) Reject H₀. There is insufficient evidence to conclude that β₂ is significant.

(b) Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.   

(c) Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

(d) Reject H₀. There is sufficient evidence to conclude that β₂ is significant.

3e. Should x₂ be dropped from the model?

Yes

No

An ASPCA statistic stated that 31% of cat owners obtain their felines from animal shelters/humane societies. I believe this has increased since this statistic was published. To test my claim, I asked 100 cat owners if they obtained their felines from animal shelters/humane societies, and 62 of them said yes. I will test this at the 0.05 significance level.

Coca Cola would like to test the effectiveness of an online advertising campaign it is currently running. Two random samples, each of 300 participants, were recruited for the study in Atlanta. One group was shown the advertisement. Then attitudes towards Coca Cola products were measured for respondents in both groups.

-Identify the IV(s) and DV(s) in the experiment

- What type of experimental design is used? (pre-experimental, true experimental, Quasi-experimental, statistical, etc)

- What are the potential threats to internal and external validity in the experiment?

Question 3

Due to the competition from Pepsi, Coca-Cola attempted to change its old recipe. Surveys of Pepsi drinkers indicated that they preferred Pepsi because it was sweeter than Coke. As a part of the analysis that led to Coke’s ill-fated move, the management of Coca-Cola performed extensive surveys in which consumers tasted various versions of the new Coke. Suppose that a random sample of 200 cola drinkers was given various versions of the Coke with different amount of sugar. After tasting the product, each drinker was asked to rate the taste quality. The possible responses were as follows:

1=poor; 2 = fair; 3 = average; 4 = good; 5 = excellent.

The responses (ratings) and sugar content (percentage by volume) of the version tested are given below

(e) Construct and interpret the 95% confidence interval for β1

(f) Predict the expected rating of Coca-Cola for the sugar level of 9 (percentage per volume).

(g) How much is the coefficient of determination and interpret it?

(h) How much is adjusted R-square? When do you use adjusted R-square?

( I ) How much is the standard error of the estimate? Is it a good model based on this criterion?

55)

A) In how many dierent ways can the letters of the word 'JUDGE' be arranged such that the vowels

always come together?

B) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5

and none of the digits is repeated?

C) In how many ways can 10 engineers and 4 doctors be seated at a round table without any restriction?

D) In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors sit

together?